{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discrete Choice Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fair's Affair data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A survey of women only was conducted in 1974 by *Redbook* asking about extramarital affairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import logit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Fair, Ray. 1978. \"A Theory of Extramarital Affairs,\" `Journal of Political\n",
      "Economy`, February, 45-61.\n",
      "\n",
      "The data is available at http://fairmodel.econ.yale.edu/rayfair/pdf/2011b.htm\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.fair.SOURCE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "::\n",
      "\n",
      "    Number of observations: 6366\n",
      "    Number of variables: 9\n",
      "    Variable name definitions:\n",
      "\n",
      "        rate_marriage   : How rate marriage, 1 = very poor, 2 = poor, 3 = fair,\n",
      "                        4 = good, 5 = very good\n",
      "        age             : Age\n",
      "        yrs_married     : No. years married. Interval approximations. See\n",
      "                        original paper for detailed explanation.\n",
      "        children        : No. children\n",
      "        religious       : How relgious, 1 = not, 2 = mildly, 3 = fairly,\n",
      "                        4 = strongly\n",
      "        educ            : Level of education, 9 = grade school, 12 = high\n",
      "                        school, 14 = some college, 16 = college graduate,\n",
      "                        17 = some graduate school, 20 = advanced degree\n",
      "        occupation      : 1 = student, 2 = farming, agriculture; semi-skilled,\n",
      "                        or unskilled worker; 3 = white-colloar; 4 = teacher\n",
      "                        counselor social worker, nurse; artist, writers;\n",
      "                        technician, skilled worker, 5 = managerial,\n",
      "                        administrative, business, 6 = professional with\n",
      "                        advanced degree\n",
      "        occupation_husb : Husband's occupation. Same as occupation.\n",
      "        affairs         : measure of time spent in extramarital affairs\n",
      "\n",
      "    See the original paper for more details.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print( sm.datasets.fair.NOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dta = sm.datasets.fair.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   rate_marriage   age  yrs_married  children  religious  educ  occupation  \\\n",
      "0            3.0  32.0          9.0       3.0        3.0  17.0         2.0   \n",
      "1            3.0  27.0         13.0       3.0        1.0  14.0         3.0   \n",
      "2            4.0  22.0          2.5       0.0        1.0  16.0         3.0   \n",
      "3            4.0  37.0         16.5       4.0        3.0  16.0         5.0   \n",
      "4            5.0  27.0          9.0       1.0        1.0  14.0         3.0   \n",
      "5            4.0  27.0          9.0       0.0        2.0  14.0         3.0   \n",
      "6            5.0  37.0         23.0       5.5        2.0  12.0         5.0   \n",
      "7            5.0  37.0         23.0       5.5        2.0  12.0         2.0   \n",
      "8            3.0  22.0          2.5       0.0        2.0  12.0         3.0   \n",
      "9            3.0  27.0          6.0       0.0        1.0  16.0         3.0   \n",
      "\n",
      "   occupation_husb   affairs  affair  \n",
      "0              5.0  0.111111     1.0  \n",
      "1              4.0  3.230769     1.0  \n",
      "2              5.0  1.400000     1.0  \n",
      "3              5.0  0.727273     1.0  \n",
      "4              4.0  4.666666     1.0  \n",
      "5              4.0  4.666666     1.0  \n",
      "6              4.0  0.852174     1.0  \n",
      "7              3.0  1.826086     1.0  \n",
      "8              3.0  4.799999     1.0  \n",
      "9              5.0  1.333333     1.0  \n"
     ]
    }
   ],
   "source": [
    "dta['affair'] = (dta['affairs'] > 0).astype(float)\n",
    "print(dta.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       rate_marriage          age  yrs_married     children    religious  \\\n",
      "count    6366.000000  6366.000000  6366.000000  6366.000000  6366.000000   \n",
      "mean        4.109645    29.082862     9.009425     1.396874     2.426170   \n",
      "std         0.961430     6.847882     7.280120     1.433471     0.878369   \n",
      "min         1.000000    17.500000     0.500000     0.000000     1.000000   \n",
      "25%         4.000000    22.000000     2.500000     0.000000     2.000000   \n",
      "50%         4.000000    27.000000     6.000000     1.000000     2.000000   \n",
      "75%         5.000000    32.000000    16.500000     2.000000     3.000000   \n",
      "max         5.000000    42.000000    23.000000     5.500000     4.000000   \n",
      "\n",
      "              educ   occupation  occupation_husb      affairs       affair  \n",
      "count  6366.000000  6366.000000      6366.000000  6366.000000  6366.000000  \n",
      "mean     14.209865     3.424128         3.850141     0.705374     0.322495  \n",
      "std       2.178003     0.942399         1.346435     2.203374     0.467468  \n",
      "min       9.000000     1.000000         1.000000     0.000000     0.000000  \n",
      "25%      12.000000     3.000000         3.000000     0.000000     0.000000  \n",
      "50%      14.000000     3.000000         4.000000     0.000000     0.000000  \n",
      "75%      16.000000     4.000000         5.000000     0.484848     1.000000  \n",
      "max      20.000000     6.000000         6.000000    57.599991     1.000000  \n"
     ]
    }
   ],
   "source": [
    "print(dta.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.545314\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "affair_mod = logit(\"affair ~ occupation + educ + occupation_husb\"\n",
    "                   \"+ rate_marriage + age + yrs_married + children\"\n",
    "                   \" + religious\", dta).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                 affair   No. Observations:                 6366\n",
      "Model:                          Logit   Df Residuals:                     6357\n",
      "Method:                           MLE   Df Model:                            8\n",
      "Date:                Tue, 24 Dec 2019   Pseudo R-squ.:                  0.1327\n",
      "Time:                        14:49:03   Log-Likelihood:                -3471.5\n",
      "converged:                       True   LL-Null:                       -4002.5\n",
      "Covariance Type:            nonrobust   LLR p-value:                5.807e-224\n",
      "===================================================================================\n",
      "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept           3.7257      0.299     12.470      0.000       3.140       4.311\n",
      "occupation          0.1602      0.034      4.717      0.000       0.094       0.227\n",
      "educ               -0.0392      0.015     -2.533      0.011      -0.070      -0.009\n",
      "occupation_husb     0.0124      0.023      0.541      0.589      -0.033       0.057\n",
      "rate_marriage      -0.7161      0.031    -22.784      0.000      -0.778      -0.655\n",
      "age                -0.0605      0.010     -5.885      0.000      -0.081      -0.040\n",
      "yrs_married         0.1100      0.011     10.054      0.000       0.089       0.131\n",
      "children           -0.0042      0.032     -0.134      0.893      -0.066       0.058\n",
      "religious          -0.3752      0.035    -10.792      0.000      -0.443      -0.307\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "print(affair_mod.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How well are we predicting?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3882.,  431.],\n",
       "       [1326.,  727.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.pred_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients of the discrete choice model do not tell us much. What we're after is marginal effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Logit Marginal Effects       \n",
      "=====================================\n",
      "Dep. Variable:                 affair\n",
      "Method:                          dydx\n",
      "At:                           overall\n",
      "===================================================================================\n",
      "                     dy/dx    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "occupation          0.0293      0.006      4.744      0.000       0.017       0.041\n",
      "educ               -0.0072      0.003     -2.538      0.011      -0.013      -0.002\n",
      "occupation_husb     0.0023      0.004      0.541      0.589      -0.006       0.010\n",
      "rate_marriage      -0.1308      0.005    -26.891      0.000      -0.140      -0.121\n",
      "age                -0.0110      0.002     -5.937      0.000      -0.015      -0.007\n",
      "yrs_married         0.0201      0.002     10.327      0.000       0.016       0.024\n",
      "children           -0.0008      0.006     -0.134      0.893      -0.012       0.011\n",
      "religious          -0.0685      0.006    -11.119      0.000      -0.081      -0.056\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "mfx = affair_mod.get_margeff()\n",
    "print(mfx.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate_marriage       4.000000\n",
      "age                37.000000\n",
      "yrs_married        23.000000\n",
      "children            3.000000\n",
      "religious           3.000000\n",
      "educ               12.000000\n",
      "occupation          3.000000\n",
      "occupation_husb     4.000000\n",
      "affairs             0.521739\n",
      "affair              1.000000\n",
      "Name: 1000, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "respondent1000 = dta.iloc[1000]\n",
    "print(respondent1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 3.0, 2: 12.0, 3: 4.0, 4: 4.0, 5: 37.0, 6: 23.0, 7: 3.0, 8: 3.0, 0: 1}\n"
     ]
    }
   ],
   "source": [
    "resp = dict(zip(range(1,9), respondent1000[[\"occupation\", \"educ\",\n",
    "                                            \"occupation_husb\", \"rate_marriage\",\n",
    "                                            \"age\", \"yrs_married\", \"children\",\n",
    "                                            \"religious\"]].tolist()))\n",
    "resp.update({0 : 1})\n",
    "print(resp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Logit Marginal Effects       \n",
      "=====================================\n",
      "Dep. Variable:                 affair\n",
      "Method:                          dydx\n",
      "At:                           overall\n",
      "===================================================================================\n",
      "                     dy/dx    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "occupation          0.0400      0.008      4.711      0.000       0.023       0.057\n",
      "educ               -0.0098      0.004     -2.537      0.011      -0.017      -0.002\n",
      "occupation_husb     0.0031      0.006      0.541      0.589      -0.008       0.014\n",
      "rate_marriage      -0.1788      0.008    -22.743      0.000      -0.194      -0.163\n",
      "age                -0.0151      0.003     -5.928      0.000      -0.020      -0.010\n",
      "yrs_married         0.0275      0.003     10.256      0.000       0.022       0.033\n",
      "children           -0.0011      0.008     -0.134      0.893      -0.017       0.014\n",
      "religious          -0.0937      0.009    -10.722      0.000      -0.111      -0.077\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "mfx = affair_mod.get_margeff(atexog=resp)\n",
    "print(mfx.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`predict` expects a `DataFrame` since `patsy` is used to select columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000    0.518782\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "respondent1000 = dta.iloc[[1000]]\n",
    "affair_mod.predict(respondent1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07516159285057666"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.fittedvalues[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5187815572121505"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.model.cdf(affair_mod.fittedvalues[1000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"correct\" model here is likely the Tobit model. We have an work in progress branch \"tobit-model\" on github, if anyone is interested in censored regression models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Logit vs Probit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "support = np.linspace(-6, 6, 1000)\n",
    "ax.plot(support, stats.logistic.cdf(support), 'r-', label='Logistic')\n",
    "ax.plot(support, stats.norm.cdf(support), label='Probit')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "support = np.linspace(-6, 6, 1000)\n",
    "ax.plot(support, stats.logistic.pdf(support), 'r-', label='Logistic')\n",
    "ax.plot(support, stats.norm.pdf(support), label='Probit')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the estimates of the Logit Fair model above to a Probit model. Does the prediction table look better? Much difference in marginal effects?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalized Linear Model Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Jeff Gill's `Generalized Linear Models: A Unified Approach`\n",
      "\n",
      "http://jgill.wustl.edu/research/books.html\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.SOURCE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This data is on the California education policy and outcomes (STAR program\n",
      "results for 1998.  The data measured standardized testing by the California\n",
      "Department of Education that required evaluation of 2nd - 11th grade students\n",
      "by the the Stanford 9 test on a variety of subjects.  This dataset is at\n",
      "the level of the unified school district and consists of 303 cases.  The\n",
      "binary response variable represents the number of 9th graders scoring\n",
      "over the national median value on the mathematics exam.\n",
      "\n",
      "The data used in this example is only a subset of the original source.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.DESCRLONG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "::\n",
      "\n",
      "    Number of Observations - 303 (counties in California).\n",
      "\n",
      "    Number of Variables - 13 and 8 interaction terms.\n",
      "\n",
      "    Definition of variables names::\n",
      "\n",
      "        NABOVE   - Total number of students above the national median for the\n",
      "                   math section.\n",
      "        NBELOW   - Total number of students below the national median for the\n",
      "                   math section.\n",
      "        LOWINC   - Percentage of low income students\n",
      "        PERASIAN - Percentage of Asian student\n",
      "        PERBLACK - Percentage of black students\n",
      "        PERHISP  - Percentage of Hispanic students\n",
      "        PERMINTE - Percentage of minority teachers\n",
      "        AVYRSEXP - Sum of teachers' years in educational service divided by the\n",
      "                number of teachers.\n",
      "        AVSALK   - Total salary budget including benefits divided by the number\n",
      "                   of full-time teachers (in thousands)\n",
      "        PERSPENK - Per-pupil spending (in thousands)\n",
      "        PTRATIO  - Pupil-teacher ratio.\n",
      "        PCTAF    - Percentage of students taking UC/CSU prep courses\n",
      "        PCTCHRT  - Percentage of charter schools\n",
      "        PCTYRRND - Percentage of year-round schools\n",
      "\n",
      "        The below variables are interaction terms of the variables defined\n",
      "        above.\n",
      "\n",
      "        PERMINTE_AVYRSEXP\n",
      "        PEMINTE_AVSAL\n",
      "        AVYRSEXP_AVSAL\n",
      "        PERSPEN_PTRATIO\n",
      "        PERSPEN_PCTAF\n",
      "        PTRATIO_PCTAF\n",
      "        PERMINTE_AVTRSEXP_AVSAL\n",
      "        PERSPEN_PTRATIO_PCTAF\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.NOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP',\n",
      "       'PERMINTE', 'AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF',\n",
      "       'PCTCHRT', 'PCTYRRND', 'PERMINTE_AVYRSEXP', 'PERMINTE_AVSAL',\n",
      "       'AVYRSEXP_AVSAL', 'PERSPEN_PTRATIO', 'PERSPEN_PCTAF', 'PTRATIO_PCTAF',\n",
      "       'PERMINTE_AVYRSEXP_AVSAL', 'PERSPEN_PTRATIO_PCTAF'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "dta = sm.datasets.star98.load_pandas().data\n",
    "print(dta.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   NABOVE  NBELOW    LOWINC   PERASIAN   PERBLACK    PERHISP   PERMINTE\n",
      "0   452.0   355.0  34.39730  23.299300  14.235280  11.411120  15.918370\n",
      "1   144.0    40.0  17.36507  29.328380   8.234897   9.314884  13.636360\n",
      "2   337.0   234.0  32.64324   9.226386  42.406310  13.543720  28.834360\n",
      "3   395.0   178.0  11.90953  13.883090   3.796973  11.443110  11.111110\n",
      "4     8.0    57.0  36.88889  12.187500  76.875000   7.604167  43.589740\n",
      "5  1348.0   899.0  20.93149  28.023510   4.643221  13.808160  15.378490\n",
      "6   477.0   887.0  53.26898   8.447858  19.374830  37.905330  25.525530\n",
      "7   565.0   347.0  15.19009   3.665781   2.649680  13.092070   6.203008\n",
      "8   205.0   320.0  28.21582  10.430420   6.786374  32.334300  13.461540\n",
      "9   469.0   598.0  32.77897  17.178310  12.484930  28.323290  27.259890\n"
     ]
    }
   ],
   "source": [
    "print(dta[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PERMINTE']].head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   AVYRSEXP    AVSALK  PERSPENK   PTRATIO     PCTAF  PCTCHRT   PCTYRRND\n",
      "0  14.70646  59.15732  4.445207  21.71025  57.03276      0.0  22.222220\n",
      "1  16.08324  59.50397  5.267598  20.44278  64.62264      0.0   0.000000\n",
      "2  14.59559  60.56992  5.482922  18.95419  53.94191      0.0   0.000000\n",
      "3  14.38939  58.33411  4.165093  21.63539  49.06103      0.0   7.142857\n",
      "4  13.90568  63.15364  4.324902  18.77984  52.38095      0.0   0.000000\n",
      "5  14.97755  66.97055  3.916104  24.51914  44.91578      0.0   2.380952\n",
      "6  14.67829  57.62195  4.270903  22.21278  32.28916      0.0  12.121210\n",
      "7  13.66197  63.44740  4.309734  24.59026  30.45267      0.0   0.000000\n",
      "8  16.41760  57.84564  4.527603  21.74138  22.64574      0.0   0.000000\n",
      "9  12.51864  57.80141  4.648917  20.26010  26.07099      0.0   0.000000\n"
     ]
    }
   ],
   "source": [
    "print(dta[['AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF', 'PCTCHRT', 'PCTYRRND']].head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = 'NABOVE + NBELOW ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT '\n",
    "formula += '+ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Aside: Binomial distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Toss a six-sided die 5 times, what's the probability of exactly 2 fours?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16075102880658435"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom(5, 1./6).pmf(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1607510288065844"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.special import comb\n",
    "comb(5,2) * (1/6.)**2 * (5/6.)**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import glm\n",
    "glm_mod = glm(formula, dta, family=sm.families.Binomial()).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  Generalized Linear Model Regression Results                   \n",
      "================================================================================\n",
      "Dep. Variable:     ['NABOVE', 'NBELOW']   No. Observations:                  303\n",
      "Model:                              GLM   Df Residuals:                      282\n",
      "Model Family:                  Binomial   Df Model:                           20\n",
      "Link Function:                    logit   Scale:                          1.0000\n",
      "Method:                            IRLS   Log-Likelihood:                -2998.6\n",
      "Date:                  Tue, 24 Dec 2019   Deviance:                       4078.8\n",
      "Time:                          14:50:24   Pearson chi2:                 4.05e+03\n",
      "No. Iterations:                       5                                         \n",
      "Covariance Type:              nonrobust                                         \n",
      "============================================================================================\n",
      "                               coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "Intercept                    2.9589      1.547      1.913      0.056      -0.073       5.990\n",
      "LOWINC                      -0.0168      0.000    -38.749      0.000      -0.018      -0.016\n",
      "PERASIAN                     0.0099      0.001     16.505      0.000       0.009       0.011\n",
      "PERBLACK                    -0.0187      0.001    -25.182      0.000      -0.020      -0.017\n",
      "PERHISP                     -0.0142      0.000    -32.818      0.000      -0.015      -0.013\n",
      "PCTCHRT                      0.0049      0.001      3.921      0.000       0.002       0.007\n",
      "PCTYRRND                    -0.0036      0.000    -15.878      0.000      -0.004      -0.003\n",
      "PERMINTE                     0.2545      0.030      8.498      0.000       0.196       0.313\n",
      "AVYRSEXP                     0.2407      0.057      4.212      0.000       0.129       0.353\n",
      "PERMINTE:AVYRSEXP           -0.0141      0.002     -7.391      0.000      -0.018      -0.010\n",
      "AVSALK                       0.0804      0.014      5.775      0.000       0.053       0.108\n",
      "PERMINTE:AVSALK             -0.0040      0.000     -8.450      0.000      -0.005      -0.003\n",
      "AVYRSEXP:AVSALK             -0.0039      0.001     -4.059      0.000      -0.006      -0.002\n",
      "PERMINTE:AVYRSEXP:AVSALK     0.0002   2.99e-05      7.428      0.000       0.000       0.000\n",
      "PERSPENK                    -1.9522      0.317     -6.162      0.000      -2.573      -1.331\n",
      "PTRATIO                     -0.3341      0.061     -5.453      0.000      -0.454      -0.214\n",
      "PERSPENK:PTRATIO             0.0917      0.015      6.321      0.000       0.063       0.120\n",
      "PCTAF                       -0.1690      0.033     -5.169      0.000      -0.233      -0.105\n",
      "PERSPENK:PCTAF               0.0490      0.007      6.574      0.000       0.034       0.064\n",
      "PTRATIO:PCTAF                0.0080      0.001      5.362      0.000       0.005       0.011\n",
      "PERSPENK:PTRATIO:PCTAF      -0.0022      0.000     -6.445      0.000      -0.003      -0.002\n",
      "============================================================================================\n"
     ]
    }
   ],
   "source": [
    "print(glm_mod.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of trials "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       807.0\n",
       "1       184.0\n",
       "2       571.0\n",
       "3       573.0\n",
       "4        65.0\n",
       "5      2247.0\n",
       "6      1364.0\n",
       "7       912.0\n",
       "8       525.0\n",
       "9      1067.0\n",
       "10     3016.0\n",
       "11      235.0\n",
       "12      556.0\n",
       "13      688.0\n",
       "14      252.0\n",
       "15      925.0\n",
       "16      377.0\n",
       "17       69.0\n",
       "18     1092.0\n",
       "19      115.0\n",
       "20      139.0\n",
       "21      449.0\n",
       "22      309.0\n",
       "23      116.0\n",
       "24       81.0\n",
       "25       66.0\n",
       "26     1259.0\n",
       "27      190.0\n",
       "28      322.0\n",
       "29     2394.0\n",
       "        ...  \n",
       "273     120.0\n",
       "274     224.0\n",
       "275     733.0\n",
       "276     120.0\n",
       "277     135.0\n",
       "278     776.0\n",
       "279     207.0\n",
       "280      41.0\n",
       "281      43.0\n",
       "282     259.0\n",
       "283     342.0\n",
       "284     250.0\n",
       "285    1750.0\n",
       "286     150.0\n",
       "287     134.0\n",
       "288      53.0\n",
       "289     266.0\n",
       "290     304.0\n",
       "291    1338.0\n",
       "292    1170.0\n",
       "293    1431.0\n",
       "294     248.0\n",
       "295     516.0\n",
       "296     591.0\n",
       "297      59.0\n",
       "298     342.0\n",
       "299     154.0\n",
       "300     595.0\n",
       "301     709.0\n",
       "302     156.0\n",
       "Length: 303, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glm_mod.model.data.orig_endog.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       470.732584\n",
       "1       138.266178\n",
       "2       285.832629\n",
       "3       392.702917\n",
       "4        20.963146\n",
       "5      1543.545102\n",
       "6       454.209651\n",
       "7       598.497867\n",
       "8       261.720305\n",
       "9       540.687237\n",
       "10      722.479333\n",
       "11      203.583934\n",
       "12      258.167040\n",
       "13      303.902616\n",
       "14      168.330747\n",
       "15      684.393625\n",
       "16      195.911948\n",
       "17       29.285268\n",
       "18      616.911004\n",
       "19       68.139395\n",
       "20       48.369683\n",
       "21      253.303415\n",
       "22      154.420779\n",
       "23       41.360255\n",
       "24       16.809362\n",
       "25       12.057599\n",
       "26      565.702043\n",
       "27       91.247771\n",
       "28      193.088229\n",
       "29     1408.837645\n",
       "          ...     \n",
       "273      47.775769\n",
       "274      63.404739\n",
       "275     297.019427\n",
       "276      36.144700\n",
       "277      35.640558\n",
       "278     343.034529\n",
       "279      83.929791\n",
       "280      16.140299\n",
       "281      23.773918\n",
       "282      36.529829\n",
       "283      60.021489\n",
       "284      48.727397\n",
       "285     704.464980\n",
       "286      31.525238\n",
       "287      13.014093\n",
       "288      33.470295\n",
       "289      68.855461\n",
       "290     174.264199\n",
       "291     827.377548\n",
       "292     506.242734\n",
       "293     958.896993\n",
       "294     187.988967\n",
       "295     259.823500\n",
       "296     379.553974\n",
       "297      17.656181\n",
       "298     111.464708\n",
       "299      61.037884\n",
       "300     235.517446\n",
       "301     290.952508\n",
       "302      53.312851\n",
       "Length: 303, dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glm_mod.fittedvalues * glm_mod.model.data.orig_endog.sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First differences: We hold all explanatory variables constant at their means and manipulate the percentage of low income households to assess its impact\n",
    "on the response variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "exog = glm_mod.model.data.orig_exog # get the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         41.409877\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means25 = exog.mean()\n",
    "print(means25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         26.683040\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means25['LOWINC'] = exog['LOWINC'].quantile(.25)\n",
    "print(means25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         55.460075\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means75 = exog.mean()\n",
    "means75['LOWINC'] = exog['LOWINC'].quantile(.75)\n",
    "print(means75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, `predict` expects a `DataFrame` since `patsy` is used to select columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "resp25 = glm_mod.predict(pd.DataFrame(means25).T)\n",
    "resp75 = glm_mod.predict(pd.DataFrame(means75).T)\n",
    "diff = resp75 - resp25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interquartile first difference for the percentage of low income households in a school district is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-11.8863%\n"
     ]
    }
   ],
   "source": [
    "print(\"%2.4f%%\" % (diff[0]*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "nobs = glm_mod.nobs\n",
    "y = glm_mod.model.endog\n",
    "yhat = glm_mod.mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.api import abline_plot\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, ylabel='Observed Values', xlabel='Fitted Values')\n",
    "ax.scatter(yhat, y)\n",
    "y_vs_yhat = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit()\n",
    "fig = abline_plot(model_results=y_vs_yhat, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot fitted values vs Pearson residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pearson residuals are defined to be\n",
    "\n",
    "$$\\frac{(y - \\mu)}{\\sqrt{(var(\\mu))}}$$\n",
    "\n",
    "where var is typically determined by the family. E.g., binomial variance is $np(1 - p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, title='Residual Dependence Plot', xlabel='Fitted Values',\n",
    "                          ylabel='Pearson Residuals')\n",
    "ax.scatter(yhat, stats.zscore(glm_mod.resid_pearson))\n",
    "ax.axis('tight')\n",
    "ax.plot([0.0, 1.0],[0.0, 0.0], 'k-');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Histogram of standardized deviance residuals with Kernel Density Estimate overlaid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The definition of the deviance residuals depends on the family. For the Binomial distribution this is\n",
    "\n",
    "$$r_{dev} = sign\\left(Y-\\mu\\right)*\\sqrt{2n(Y\\log\\frac{Y}{\\mu}+(1-Y)\\log\\frac{(1-Y)}{(1-\\mu)}}$$\n",
    "\n",
    "They can be used to detect ill-fitting covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    }
   ],
   "source": [
    "resid = glm_mod.resid_deviance\n",
    "resid_std = stats.zscore(resid)\n",
    "kde_resid = sm.nonparametric.KDEUnivariate(resid_std)\n",
    "kde_resid.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, title=\"Standardized Deviance Residuals\")\n",
    "ax.hist(resid_std, bins=25, density=True);\n",
    "ax.plot(kde_resid.support, kde_resid.density, 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### QQ-plot of deviance residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "fig = sm.graphics.qqplot(resid, line='r', ax=ax)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
